As
you will see, The Teaching Gap compares mathematics instruction in the United
States, Japan, and Germany on the basis of data collected through the Third
International Mathematics and Science Study (TIMSS). You might be surprised (or
not) that the United States does not compare favorably. But it is important
that you understand that The
Teaching Gap is not about a
contest. Rather it is about trying to learn more about us by examining
instruction in other countries. As Stigler and Hiebert say repeatedly,
mathematics instruction is a cultural phenomenon, and coming to understand
one's culture is like a fish coming to understand water. An organism cannot
notice its all-pervasive environment until it experiences life outside it. Our
educational culture is so pervasive that there are important aspects of it that
we cannot notice without experiencing cultures having aspects that differ from
ours. So, please read The
Teaching Gap in that spirit --
as an attempt to help us step out of our culture of mathematics teaching in
order to examine it more objectively.

Reflective
Essay

Please
respond to these questions after reading The
Teaching Gap.

1)The authors
describe large variations across US, Germany and Japanese teaching cultures and
little variation within cultures.

a)Describe the
teaching cultures in each country and the variations that exist across the
three countries.

b)Summarize the
authors’ characterization of the US teaching culture. Is their characterization
accurate? If not, how is it inaccurate?

2)a)Describe the major findings of the
Third International Mathematics and Science Study (TIMSS).

b)Describe specific
methods (see Chapter 2) that make the findings compelling. Do you believe the
findings reported? If not, what flaws in the methods may invalidate the
findings?

3)The authors of
the Teaching Gap describe “images of teaching” (see Chapter 3 and Chapter 4).
What differences among the three countries were most striking to you?

4)Explain what the
authors meant by “content coherence”. Why is this issue important?

a)Provide a brief
overview of the attributes and process of lesson study.

b)What is your view
of lesson study? Could lesson study be effectively implemented in your school?
If so, describe your view of how it could happen, noting any changes to school
structure, etc. that would be needed.

6)How did the book make you feel? How did that
feeling evolve from beginning to middle to end of the book?

Knowing and
Teaching Elementary Mathematics

This book discusses findings
from a study by Liping Ma that compares mathematical understanding among U.S.
and Chinese elementary school teachers as it relates to classroom teaching
practices.A critical finding of
the study is that Chinese teachers continue to learn mathematics and to refine
their content understandings throughout their teaching careers. Teachers are
provided support and time to regularly reflect on and deliberate about their
teaching, while U.S. teachers are not. So,
please read The Teaching Gap in that spirit -- as an attempt to help us
step out of our culture of mathematics teaching in order to examine it more
objectively.

1)The preface and
chapter 1 of Ma’s book contrast the mathematical knowledge of US teachers and
Chinese teachers.

a)What are the
primary differences that Ma describes? To what does Ma attribute these
differences?

c)What does Ma say
about the relationship between teachers’ knowledge and their teaching
practices?

d)Compare times
when you’ve taught an idea that you understood well with times when you’ve
taught an idea that you’ve understood poorly. Were you able to orchestrate more
meaningful learning experiences for your students?Explain.

2)Provide a brief
overview of Chapter 4, noting especially the differences in the knowledge and
attitudes of U.S. and Chinese teachers as they approached their teaching of a
novel topic.